Actively shielded coils offer a design alternative for magnetic resonance imaging (MRI) magnets. A theoretical basis is presented for a design approach to achieving optimized MRI magnetic configurations. A random search technique is used to select configurations using the least amount of conductor, exhibiting the smallest level of field inhomogeneity and resulting in the least level of stray field while meeting central field and size requirements. A computer program has been developed which incorporates this design approach. Magnetic configurations selected with the aid of this design tool are discussed. © 1990 IEEE